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Section 7.1 – Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30°, 45°, 60°, 120° , etc.). So, you will still need those unit circle values. We’ll use right triangle trigonometry to find the lengths of all of the sides and the measures of all of the angles. In some problems, you will be asked to find one or two specific pieces of information, but often you’ll be asked to “solve the triangle,” that is, to find all lengths and measures that were not given. Example 1: Find x and y. y x 250 10 Example 2: In ∆ABC with right angle C, ∠A = 40° and AC = 12. Find BC. Round the answer to the nearest hundredth. 1 Example 3: Draw a diagram to represent the given situation. Then find the indicated measures to the nearest tenth of a degree. An isosceles triangle has sides measuring 20 inches, 54 inches and 54 inches. What are the measures of its angles? Example 4: Draw a diagram to represent the given situation. Then find the indicated measure to the nearest tenth. A 216 foot ladder is leaned against the side of a building. If the ladder forms a 41° angle with the ground, how high up the side of the building does the ladder reach? 2 Angle of Elevation; Angle of Depression: 3 Example 5: Draw a diagram to represent the given situation. Then find the indicated measure to the nearest tenth. The angle of elevation to the top of a building from a point on the ground 125 feet away from the building is 8°. How tall is the building? Example 6: Draw a diagram to represent the given situation. Then find the indicated measure to the nearest tenth. Dave is at the top of a hill. He looks down and spots his car at a 60° angle of depression. If the hill is 48 meters high, how far is his car from the base of the hill? 4